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A New Indirect Probe of the Higgs Self-Coupling

A New Indirect Probe of the Higgs Self-Coupling. TLEP Vidyo Meeting Jan 6 th 2014. Matthew McCullough Simons Postdoctoral Fellow, MIT. Measuring the Self-Coupling. Why is it important? It is there, so we should try to constrain it

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A New Indirect Probe of the Higgs Self-Coupling

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  1. A New Indirect Probe of the Higgs Self-Coupling TLEP Vidyo Meeting Jan 6th 2014 Matthew McCullough Simons Postdoctoral Fellow, MIT

  2. Measuring the Self-Coupling • Why is it important? • It is there, so we should try to constrain it • Known Higgs mass means it is predicted in SM. Important test! • Probe of SM scalar potential, with implications for lifetime of Universe! • (See e.g. Elias-Miro et al.)

  3. Measuring the Self-Coupling • At LHC (Requires ECM > 2 mh): • At ILC (Requires ECM > 2 mh + mZ): Dolan, Englert, Spannowsky J. Tian, K. Fujii

  4. What if ECM< 2 mh + mZ? e Z • At 240 GeV: • But what if we have: • We would never know? h e

  5. What if ECM< 2 mh + mZ? • Lepton colliders are precision machines. Actually measure LO tree-level and NLO, NNLO, etc: • Can probe new physics in loops as well! • New physics = new state, modified coupling

  6. Self-Coupling at NLO • For now take simplifying (unrealistic) assumption that only self-coupling is modified: • Which would arise in EFT from

  7. Self-Coupling at NLO • At LO (tree-level) no difference: e Z h e

  8. Self-Coupling at NLO • At NLO modified coupling enters in the following loops: • And also:

  9. Self-Coupling at NLO • Can use modified self-coupling and calculate: • Does this make sense in QFT? • Yes, modified self-coupling only at LO. • If extending to NNLO need counter-term to higher-dimension operator. • Same as modified htt coupling in gluon fusion

  10. Self-Coupling at NLO • Result: • Feynarts/Formcalc/LoopTools • At TLEP sensitive to • Thus a modified self-coupling of • … would generate a deviation in the cross section measurement!

  11. Self-Coupling at NLO • Result: • At TLEP sensitive to • Thus a modified self-coupling of • Or, if there is a deviation it may be due to modified self-coupling!

  12. Self-Coupling at NLO • Sounds great, but there is a but… • In any realistic BSM scenario not just self-coupling modified. • Really measure: • Can’t “fingerprint” self-coupling from a single cross section deviation.

  13. Self-Coupling at NLO • Could make arguments about whether or not cancellations are occurring. • Or use theoretical arguments ( ) to create a one-sided bound • But there is a better way to proceed… (Mentioned in paper, but emphasized recently by Jesse Thaler)

  14. Self-Coupling at NLO • Corrections are energy-dependent • Corrections from not energy-dependent. • Combine measurements to constrain different linear combinations. • Get an ellipse-plot constraint

  15. Self-Coupling at NLO • Combining different measurements: TLEP240 +TLEP350? (Need input on cross-section precision at 350 GeV. Assuming 1% here) TLEP240 + ILC500?

  16. Self-Coupling at NLO • Combining different measurements: Can see usual 28% on plot, but much more information from multiple energies. Calculation only valid to first order in so take large deviations with pinch of salt. Note axis scale

  17. Conclusions • Previously assumed that below di-Higgs threshold, nothing could be said about Higgs self-coupling. I.e. the following scenarios are equivalent: or • This is not true.

  18. Conclusions • In fact, the following two scenarios or are distinguishable due to NLO effects. • Indirect constraint has ambiguity • Measurements at multiple energies can lead to ellipse-plot constraints.

  19. Conclusions • In future, could be looking at plots like:

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